Linear Programming-Graphical Method and Simplex Method of Solutions [Optionals IAS Mains Mathematics]: Questions 1 - 7 of 11
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Question 1
Appeared in Year: 2016
Describe in Detail
Essay▾Find the maximum value of with constrains , , by graphical method. [CS (Main) Paper 2]
Explanation
- Given with constrains , ,
- For graph, we convert the inequalities into equation.
and
- In equation
If
- Then
Point is
If
- Then
point is
- In equation
- If then
Point is
- If then
Point is
- Plotting these equations on the graph. Area of in the figure satisfied by the constraint is shown by the shaded area and is called…
… (56 more words) …
Question 2
Appeared in Year: 2016
Describe in Detail
Essay▾Maximize subject to is the optional solution unique justify your answer. [CS (Main) Paper 2]
Explanation
- After introducing slack variable in the constraint, we convert inequalities into equalities, and assign coefficient to slack variable in the objective function. The resultant objective function and constraint equation are given below.
Subject to
- The table for simplex computation are shown below.
- Since all the elements of Cj-Zj row are or zero, so w…
… (51 more words) …
Question 3
Appeared in Year: 2012
Describe in Detail
Essay▾For each hour per day that Ashok studies mathematics, it yields him 10 marks and for each hour that he studies physics, it yields him 5 marks. He can study at most 14 hours a day and he must get at least 40 marks in each. Determine graphically how many hours a day he should study mathematics and physics each, in order to maximize his marks? (CS paper -2)
Explanation
Let be the number of hour he study mathematics and y be the number of hour he study physics
Max (marks function)
Subject to
Where
Now, in order to plot the graph, we convert the inequalities into equation.
… eq. (i)
And
… eq. (ii)
And 3) … eq. (iii)
Any Combination of value of x and y which satisfies the given constr…
… (69 more words) …
Question 4
Appeared in Year: 2007
Describe in Detail
Essay▾Solve the following by simplex method
Maximize
Subject to
(CS paper -2)
Explanation
Given problem is
Maximize
Subject to
We introduce slack variables and convert constraints into equation and assign ‘o’ co-efficient to the slack variables in the objective function.
Max
Subject to
Simplex Table 1
Simplex Table 2
Simplex Table 3
Simplex Table 4
Since all
So optimal solution is obtained
… (41 more words) …
Question 5
Appeared in Year: 2013
Describe in Detail
Essay▾Minimize
Subject to the constraints
(CS paper -2)
Explanation
Given
Minimize
Maximize
Subject to the constraints
Table 1
Table 2
Table 3
Since all the values of
So optimal solution obtained
… (35 more words) …
Question 6
Appeared in Year: 2013
Describe in Detail
Essay▾Maximize
Subjected to
And (CS paper -2)
Explanation
Given max
Subjected to
And
We introduce surplus and artificial variable and assign O co-efficient to surplus to artificial variable. The resultant objective function and constraint are given as under:
Max
Where
Table 1
Table 2
Table 3
Since all the values of
So optimal solution obtained
… (35 more words) …
Question 7
Appeared in Year: 2011
Describe in Detail
Essay▾Solve by simplex method, the following LP problem:
Maximize,
Constraints,
(CS paper -2)
Explanation
Given
Maximize,
Constraints,
We introduce slack variables and convert constraints into equation and assign ‘o’
Coefficient to the slack variable in the objective function
Max
Subject to
Where
Simplex Table 1
Simplex Table 2
Simplex Table 3
Since all the
So optimal solution obtained
Max
… (21 more words) …